She claims that she will only be punished for a certain amount of time., then allowed into paradise, bit like a prison term. I can't argue that point as whilst I think I know more about religion than the average person, I would claim relative ignorance of Islam. Is this a concept you are aware of?
I think she is struggling quite a bit which is why she gets very angry. As an example with Israel, her views border on anti-Semitism(although I daren't suggest that) and is totally closed to any blame being apportioned to Hamas. I think she's having real issues in her head but if I suggest conflicting emotions I get shouted down!! :-)
Your friend sounds very confused, and yes, most definitely suffering from a severe case of cognitive dissonance. In my experience, it is often those who are least sure about their own beliefs (and are unable to really self examine why they need to keep them at all) who get most annoyed at anyone pointing out the ridiculousness of those beliefs.
I'd recommend that you avoid bringing up the topic with her, and let her go at her own pace. If anything, if she were my friend, I'd just ask her questions instead of trying to teach her, which will only make her more defensive. Ask her for citations of the things she claims about Islam. Basically, in some friendly ways, ask her to really read Islamic scriptures for herself, and look up what they say about things like hell, eternal torture, the character of Muhammad, etc.
If she is intelligent, she'll figure out for herself as she reads more and more Islamic scriptures, that it's as much hogwash as the Bible and other mythological texts. And that she need not cling to religion to have an identity. She obviously doesn't actually believe in what they say; she only seems to be very misinformed or keeping herself from getting fully versed in what Islamic scriptures actually say. Gently encourage her to learn what Islamic canon is, for herself.
Topic: Hello From Kent